A LAN is an acronym for Local Area Network.
LANs are groups of computers that are hooked together in a small geographical area. There is no exact definition on what is a LAN vs other sizes of networks, but basically it is when the computers are in the same basic area.
If you are connected to the Internet at home and use more than one device to use that Internet connection, you have a LAN. The devices could be PCs, laptops, game boxes. Tablets, smart phones or other devices. They are all in a small geographical location connected together (wireless or wired). They may be sharing devices, for instance a printer, or you may be sharing files.
The computers that are connected/networked together in a business or plant would be in a LAN. The LAN may cover one building or several buildings. If some of the devices are in another city or state, then it is not considered a local area network. If they are in several buildings across a city they may be considered in a LAN or sometimes (not used as often as a name) a MAN (Metropolitan Area Network).
In the larger cities, a LAN may be the network on just one floor in an office building or it may cover several floors.
Basically, a LAN is when the computers are considered in some way close to each other and are sharing one network.